Solve for $x$ and $y$ using substitution. ${-3x+2y = 12}$ ${y = -3x-3}$
Solution: Since $y$ has already been solved for, substitute $-3x-3$ for $y$ in the first equation. ${-3x + 2}{(-3x-3)}{= 12}$ Simplify and solve for $x$ $-3x-6x - 6 = 12$ $-9x-6 = 12$ $-9x-6{+6} = 12{+6}$ $-9x = 18$ $\dfrac{-9x}{{-9}} = \dfrac{18}{{-9}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -3x-3}\thinspace$ to find $y$ ${y = -3}{(-2)}{ - 3}$ $y = 6 - 3$ $y = 3$ You can also plug ${x = -2}$ into $\thinspace {-3x+2y = 12}\thinspace$ and get the same answer for $y$ : ${-3}{(-2)}{ + 2y = 12}$ ${y = 3}$